A Novel Approach for Analytical Model of Metal-Metal Functionally Graded Circular Beam

Functionally graded materials are advanced inhomogeneous materials in which element gradation changes continuously and smoothly from one phase to the other. The purpose of this study is to derive a novel and flexible model for metal-metal functionally graded circular beams. By means of this novel model, it is possible to determine the displacements numerically under all kinds of loading as well as to perform both elastic and plastic stress analysis. The mathematical formulation is derived through higher-order shear deformation theory. For this purpose, macro-mechanical model of functionally graded circular beam is constructed initially. Then, kinematic relations of functionally graded circular beam are derived. Based on Hamilton's principle, a system of differential equations governing the static behavior of a functionally graded circular beam is derived. Numerical results are presented after exact solutions are obtained. The advantage of this novel model is that it is possible to define not only linear gradation but also parabolic gradation from center to the surface of the beam.